Is it possible that arithmetic quantities follow quantum mechanical rules?

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Offline David Reichard

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For example,when integrating over ever-smaller intervals,does uncertainty become a factor?If the actual size of these intervalswere stated,would the Planck size be reached?Is there uncertainty at a very small point?Could the point's location be expressed as a probability?


Offline evan_au

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When you are doing mathematical integration over a function which is uniquely defined at every point, the intervals can be infinitely small with no quantum effects. It helps greatly if the function is continuous, with continuous derivatives.

If you are trying to integrate a function which has no defined derivative, and the values are not unique (like some fractals), then there is an element of uncertainty involved, and probabilities may be one way to resolve this.

If you are trying to calculate the values of physical systems, which are subject to quantum effects, then you must include these quantum effects in your evaluation of the integral. You can use probabilities to produce an "average" answer, or more rigorous methods to produce a distribution of answers.